In a previous paper [Zhang , J. Chem. Phys. 110, 5318 (1999)] we introduced a model for polydisperse hard-sphere mixtures that is able to adjust its particle size distribution. Here we give the explanation of the questions that arose in the previous description and present a consistent theory of the phase transition in this system, based on the Percus-Yevick equation of state. The transition is continuous, and like Bose-Einstein condensation, a macroscopic aggregate is formed due to the microscopic interactions. A treatment based on the equation of state by Boublik, Mansoori, Carnahan, Starling, and Leland leads to the same conclusion with slightly more accurate predictions.